You may also like

Mathematical Issues for Chemists

A brief outline of the mathematical issues faced by chemistry students.

Reaction Rates

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

Catalyse That!

Can you work out how to produce the right amount of chemical in a temperature-dependent reaction?

Mixing pH

Age 16 to 18
Challenge Level

”‹”‹”‹”‹”‹”‹The pH of a solution is defined using logarithms as

pH = -\log_{10}[H^+],
where $[H^+]$ is the concentration of $H^+$ ions in mol/l of the solution.


  • Given that the pH of a beaker of pure water is 7, work out how many $H^+$ ions there are in 1 litre of the water.
  • A strong acid has a pH of 2. If one litre of this acid is diluted with 1 litre of water, what is the pH of the resulting solution?
  • A strong acid has a pH of 1.3. If I have 100ml of this acid, how much water needs to be added to create a solution of pH 2?
  • 400ml of an acid of pH 3 is added to 300ml of an acid of pH 4. What is the resulting pH?


Make up some of your own mixing pH questions. For example:


  • If I start with $1$ litre of acid of pH $1$, what happens to the pH each time I add $100$ml of water? What sort of curve results?
  • Is it the case that when mixing two solutions, the resulting pH is always between the pH of the two initial solutions?